Question

this is a differential equation question

please solve them with steps and details also, make sure it is correct

solve By Delay Theorem

(3 points each) Find the following functions, L{(t-1) step(t - 4)}

Answer 1

1 [lt-). It - 4)] [ 64.13?. clep/t-u] Delay theolem : for tco and [+49] = F()., 7 (t) = 0 -tos then. 1918-ci) F(s) & In this question , 2 2 11 H-1).M (4-4) (7-4+3). ult-4) [4-41-9 + 243 44-4) ult-4) l-o? ult-u) · f(t) = (t-4).cf-) (t-4.44-4) + 64-4) Melt-4) a qult-4) het ., t, lt) 6tult) tu (1) , t, (t) tz (+) 9-41t)

(ا - 4) ,1 : ({}{ رہا - + + + (۹ - f ( t + (4-4) ,1 Hence, [(2+] : + (ا -t) .1 (h-1) + [ 44 - 4 ) 1, (4-۷) [5 (1 - )) + + (: (1- ،] - [ ( - ) (h - ( +(4)] .باهله [ + ]7 (2) + ] 1 Sع [41] :[ et. al] . [ 4 ] 2 هه تاو تره [1) مد (1) - L 4. (E) S. Hence, frem theolem , the delay Sh - sho de آريا - 4) , )4 e F() 3ی ها - Sh- 29 2 [ 1 ( - ) ] ره) . e 2 کہ کا ۔ 55 - ۹e (ء) رم . د [ ; (4 - )] e S.

Hence, GS Qe LS Ee LS 9e [t] + 우 2 s2 S3 S 4 5 0 [e-i stry (t-4] 「2 ] + + e 3 5 S s2.